What happen with the conservation laws when we locally refine grids in adaptive meshes?

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Sahli Youcef Popular answer

yes

Sahli Youcef

Filippo Maria Denaro

If you properly adopt a FV formulation, the property of the unique numerical flux allow to fulfill conservation of the estensive variables. But you need to properly construct the flux on the refined grids.

Paolo Lampitella

If the new grid fully and exactly overlaps the old one, you can intersect the two and make a 1 to 1 mapping of the conserved avariables followed by a volume average on the new grid.